Non-Wilson-Fisher kinks of $O(N)$ numerical bootstrap: from the deconfined phase transition to a putative new family of CFTs

Abstract

It is well established that the O(N)O(N) Wilson-Fisher (WF) CFT sits at a kink of the numerical bounds from bootstrapping four point function of O(N)O(N) vector. Moving away from the WF kinks, there indeed exists another family of kinks (dubbed non-WF kinks) on the curve of O(N)O(N) numerical bounds. Different from the O(N)O(N) WF kinks that exist for arbitary NN in 2<d<42<d<4 dimensions, the non-WF kinks exist in arbitrary dimensions but only for a large enough N>N_c(d)N>Nc(d) in a given dimension dd. In this paper we have achieved a thorough understanding for few special cases of these non-WF kinks, which already hints interesting physics. The first case is the O(4)O(4) bootstrap in 2d, where the non-WF kink turns out to be the SU(2)_1SU(2)1 Wess-Zumino-Witten (WZW) model, and all the SU(2)_{k>2}SU(2)k>2 WZW models saturate the numerical bound on the left side of the kink. This is a mirror version of the Z_2Z2 bootstrap, where the 2d Ising CFT sits at a kink while all the other minimal models saturating the bound on the right. We further carry out dimensional continuation of the 2d SU(2)_1SU(2)1 kink towards the 3d SO(5)SO(5) deconfined phase transition. We find the kink disappears at around d=2.7d=2.7 dimensions indicating the SO(5)SO(5) deconfined phase transition is weakly first order. The second interesting observation is, the O(2)O(2) bootstrap bound does not show any kink in 2d (N_c=2Nc=2), but is surprisingly saturated by the 2d free boson CFT (also called Luttinger liquid) all the way on the numerical curve. The last case is the N=\inftyN=∞ limit, where the non-WF kink sits at (\Delta_\phi, \Delta_T)=(d-1, 2d)(Δϕ,ΔT)=(d−1,2d) in dd dimensions. We manage to write down its analytical four point function in arbitrary dimensions, which equals to the subtraction of correlation functions of a free fermion theory and generalized free theory. An important feature of this solution is the existence of a full tower of conserved higher spin current. We speculate that a new family of CFTs will emerge at non-WF kinks for finite NN, in a similar fashion as O(N)O(N) WF CFTs originating from free boson at N=\inftyN=∞.